The Georgian Interior Ministry said in a statement that automatic and mortar fire was opened early on Sunday from Abkhazia's adjacent Gali district against a police post in the village of Koki in the Zugdidi in western Georgia.
An officer from a special unit of the Georgian Interior Ministry was wounded during the fire and was taken to a Tbilisi hospital, the statement said, adding that the Georgian side did not open retaliation fire.
Observers from the European Union monitoring mission in Georgia who had visited the site declined any comment.
Meanwhile, Abkhazian Defense Minister Merab Kishmariya said that observer posts of the Abkhazian armed forces registered fire in the Zugdidi district in Georgia.
Russia recognized the independence of Abkhazia and South Ossetia, another separatist Georgian republic, on August 26. Russia and Georgia fought a five day war on August 8-12 after Georgian forces had attacked South Ossetia in a bid to bring it back under central control.